Question

From the top of a building 12 m high , the angle of elevation of the top of tower is found
be 45 and the angle of depression of the base of the towers 30. Find the height
of the tower and distance on the ground from the building​

Answer 1

Answer:

Height = 12(√3 + 1)m

Distance = 12√3m

Explanation:

From the diagram, AO = BY

angle OAY = angle AYB

OX = OA ( as the triangle AOC is isosceles)

From triangle AOY, tan 30° = YO/AO

From triangle ABY, tan 30° = AB/BY = 12/AO

From the above, we have YO/AO = 12/AO

Therefore, YO = 12m

AO= (tan 30°)(12) = 12√3m (this is the distance between the two)

As AO = XO, XO = 12√3m

Height of tower(XY) = XO + YO

= 12 + 12√3

Height = 12(√3 + 1)m

I'm sorry if I made it too complicated.......